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This paper focuses on Radio Frequency Identification (RFID) systems, whose market is tremendously growing due to the increasing need for efficient supply chain and healthcare management. Two protocols are proposed that offer mutual authentication, confidentiality, forward security, anonymity, unlinkability, scalability, and resistance against the most important security attacks. They differ in storage requirements at the server side. Both proposed protocols are very efficient as the number of required elliptic curve multiplications is limited to two at the tag side. Moreover, the schemes are also more effective and secure than other related work presented in literature. 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